I have no idea how to solve this. I love geometry, but I've found that I'm not very naturally good at it. please help!

The circles in the figure I have drawn out are concentric. The chord AB is tangent to the inner circle and has a length of 12 cm. What is the Area of of the non-shaded region? (A of big triangle - A of small triangle)Attachment 28090

Apr 22nd 2013, 04:46 PM

Plato

Re: concentric circle problem

Quote:

Originally Posted by aaronrpoole

The circles in the figure I have drawn out are concentric. The chord AB is tangent to the inner circle and has a length of 12 cm. What is the Area of of the non-shaded region? (A of big triangle - A of small triangle)Attachment 28090

I think that you need to know the radius of one of those two circles. Or some other term from that webpage.

Apr 22nd 2013, 06:35 PM

Soroban

Re: concentric circle problem

Hello, aaronrpoole!

This is a classic problem . . . with a surprising punchline.

Quote:

The circles in the figure I have drawn are concentric.
The chord AB is tangent to the inner circle and has a length of 12 cm.
What is the area of of the non-shaded region? (Area of big circle - Area of small circle)

is the center of the circles. is the midpoint of chord
Let , the radius of the large circle.
Let , the radius of the small circle.

From right triangle .[1]

The area of the large circle is:
The area of the small circle is:

The area of the ring is:

Substitute [1]: .

Surprise! .We didn't need to know the two radii.

The small circle could be a golfball or the Earth.
The area of the ring is constant!

Apr 23rd 2013, 12:41 AM

first123

Re: concentric circle problem

While this subject can be very touchy for most people, my opinion is that there has to be a middle or common ground that we all can find. I do appreciate that youve added relevant and intelligent commentary here though. Thank you!